Details

simplify42.5m

Calls

10214 calls:

Slowest
5.7s
(/ (* (* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ (* M D) (* 2 d))) (* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ (* M D) (* 2 d)))) (* (* (* (/ l h) 2) (* (/ l h) 2)) (* (/ l h) 2)))
5.4s
(/ (* (* (* l 2) (* l 2)) (* l 2)) (* (* (* (/ (* M D) (* 2 d)) h) (* (/ (* M D) (* 2 d)) h)) (* (/ (* M D) (* 2 d)) h)))
5.2s
(/ (* (* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d)))) (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d)))) (* (* (* (/ l h) 2) (* (/ l h) 2)) (* (/ l h) 2)))
5.0s
(/ (* (* (* (sqrt (- 1 (* 3 (* v v)))) (sqrt (- 1 (* 3 (* v v))))) (sqrt (- 1 (* 3 (* v v))))) (* (* (* (sqrt 2) (sqrt 2)) (sqrt 2)) (* (* (- 1 (* (* v v) (* v v))) (- 1 (* (* v v) (* v v)))) (- 1 (* (* v v) (* v v)))))) (* (* (* 4 (+ 1 (* v v))) (* 4 (+ 1 (* v v)))) (* 4 (+ 1 (* v v)))))
4.9s
(* (+ (* 1 1) (+ (* (/ (/ (* M D) (* 2 d)) (/ (* l 2) (* (/ (* M D) (* 2 d)) h))) (/ (/ (* M D) (* 2 d)) (/ (* l 2) (* (/ (* M D) (* 2 d)) h)))) (* 1 (/ (/ (* M D) (* 2 d)) (/ (* l 2) (* (/ (* M D) (* 2 d)) h)))))) (* (sqrt l) (sqrt h)))

sample9.8m

Algorithm
55×intervals
Results
2.2m240917×body80valid
1.8m21876×body1280valid
1.8m159868×body80nan
52.9s16558×body640valid
52.8s8490×body10240exit
37.6s7196×body2560valid
32.7s3324×body5120valid
19.3s8130×body320valid
9.2s8411×body160valid
3.1s620×body1280nan
2.4s614×body640nan
313.0ms346×body320nan
121.0ms182×body160nan

prune6.1m

series1.3m

Calls

417 calls:

Slowest
2.5s
(sqrt (pow (* n (* U (* 2 (+ (* (/ l Om) (* -2 l)) (- t (* (* (/ l Om) (* (/ l Om) (- U U*))) n)))))) 1))
2.2s
(cos (* (* (cbrt (* m (/ K 2))) (cbrt (- (/ (* K (+ m n)) 2) M))) (cbrt (- (/ (* K (+ m n)) 2) M))))
2.0s
(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))
1.9s
(sqrt (pow (* (* n U) (* 2 (+ (* (/ l Om) (* -2 l)) (- t (* (* (/ l Om) (* (/ l Om) (- U U*))) n))))) 1))
1.8s
(sqrt (pow (* (* n U) (* 2 (+ (* (/ l Om) (* -2 l)) (- t (* (* (* (/ l Om) (/ l Om)) (- U U*)) n))))) 1))

regimes39.0s

Accuracy

Total 49.3b remaining (29.3%)

9.0b21.2%Toniolo and Linder, Equation (13)
8.0b7.8%Maksimov and Kolovsky, Equation (3)
7.6b69.6%Toniolo and Linder, Equation (7)
6.6b49.8%Henrywood and Agarwal, Equation (3)
6.6b-8.9%Henrywood and Agarwal, Equation (13)

rewrite10.8s

Algorithm
109×rewrite-expression-head
Calls

417 calls:

Slowest
798.0ms
(* (cos (- (/ (* K (+ m n)) 2) M)) (exp (- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))))
197.0ms
(/ (+ EAccept (- (+ Ev Vef) mu)) KbT)
186.0ms
(+ (pow a 4) (* (* (* a b) (* a b)) 2))
176.0ms
(/ (- 1 (* 5 (* v v))) (* (* (* (* PI t) (* (cbrt (sqrt (* 2 (- 1 (* 3 (* v v)))))) (cbrt (sqrt (* 2 (- 1 (* 3 (* v v)))))))) (cbrt (sqrt (* 2 (- 1 (* 3 (* v v))))))) (- 1 (* v v))))
162.0ms
(+ (pow (+ (* a a) (* b b)) 2) (* 4 (+ (* (* a a) (+ 1 a)) (* (* b b) (- 1 (* 3 a))))))
Rules
8787×times-frac
4772×add-sqr-sqrt
4738×*-un-lft-identity
4698×add-cube-cbrt
2357×cbrt-prod
1420×div-inv
1304×sqrt-prod
1141×add-exp-log
1013×associate-*r*
988×add-cbrt-cube
895×associate-*r/
709×pow1
539×associate-/r/
533×sqrt-div
516×associate-/l*
476×add-log-exp
452×frac-times
415×insert-posit16
401×associate-/r*
364×cbrt-div
358×associate-*l/
336×associate-*l*
304×flip3-- flip--
230×div-exp
223×prod-exp
209×flip-+ flip3-+
191×cbrt-unprod
179×expm1-log1p-u log1p-expm1-u
172×cbrt-undiv
150×unpow-prod-down
149×frac-add
142×prod-diff
141×*-commutative
125×pow-prod-down
114×frac-2neg clear-num
102×associate-/l/
87×unpow-prod-up
81×fma-udef
77×distribute-rgt-in distribute-lft-in
67×pow1/2
57×rem-sqrt-square
55×pow-to-exp
47×difference-of-sqr-1
39×sub-neg
38×pow1/3
36×sin-mult
32×div-sub
27×pow-exp associate-+r+
26×sum-log
24×rec-exp
22×tan-quot
21×exp-prod
20×pow-prod-up
18×pow2
16×pow-pow fma-neg
15×pow-plus pow-unpow
14×associate-+r- +-commutative
13×distribute-lft-out un-div-inv
12×sqr-sin
11×distribute-lft-out-- fma-def
10×unpow2
pow-flip inv-pow
exp-diff
difference-of-squares diff-log
associate--l+ associate-+l- rem-exp-log
distribute-lft-neg-in frac-sub exp-sum distribute-rgt-neg-in log-pow acos-asin log-div
pow3
associate-+l+ neg-sub0 log-prod distribute-frac-neg cos-sum distribute-neg-frac distribute-rgt-out-- neg-mul-1 remove-posit16 pow-sub rem-log-exp
distribute-lft-neg-out cube-unmult sqrt-unprod sub-div exp-neg asin-acos rem-square-sqrt cos-diff associate--r- distribute-rgt1-in

bsearch10.8s

localize7.6s

end57.0ms